Almost Periodic Solutions And Asymptotically Almost Periodic Solutions Of Discrete Volterra Equations

For discrete Volterra equations with or without delay, we study the following Volterra systems under certain conditions.where a(n), B{n,j,x) and A(n,j,x) are given vector sequences and converge to p(n), F(n,j,x) and E(n,j,x) in some sense (see below in Section 2). Equations (3) is a limiting equation of (1), while Eq. (2) is a perturbed form of (3). we obtain sev-eral results concerning almost periodic solutions and asymptotically almost periodic solutions, bounded solutions and almost periodic solutions.Moreover, we also consider the following difference equations systems in the whole line, and obtain some relations between the almost periodic solutions and the asymptotically almost periodic solutions. where a(n), C(n,j,x) are given vector sequences and converge to p(n), D(n,j,x) in some sense.